Question

The CO2 content of the air in a 5000 cu ft room is 0.3 percent. Fresh air containing 0.1 percent CO2 is pumped into the room at teh rate of 1000 ft^3/min . A) find the percentage of CO2 in the room after 30 min. When will the CO2 content be 0.2 percent?   ANS) 0.10 percent and 3.47 minutes

Answer 1

After one minute 1000cuft air contains 0.1% CO2 and remaining 4000 cuft contains 0.3 % of CO2

so total CO2 = [(0.1x 1)+(0.3 x 4)]/5 = 0.26

after second minute the percentage of CO2 = [(0.1 x 1)+(0.26 x 4)]/5 = 0.228

similary proceed for 30 mts,you will get CO2 after 30 mts, see calculation for all 30 mts

co2 in pumped air	Present room contains co2			total co2 after replacing	CO2 percentage after replacing
0.1	0.3	4	1.2	1.3	0.26
0.1	0.26	4	1.04	1.14	0.228
0.1	0.228	4	0.912	1.012	0.2024
0.1	0.2024	4	0.8096	0.9096	0.18192
0.1	0.18192	4	0.72768	0.82768	0.165536
0.1	0.165536	4	0.662144	0.762144	0.152429
0.1	0.152429	4	0.609715	0.709715	0.141943
0.1	0.141943	4	0.567772	0.667772	0.133554
0.1	0.133554	4	0.534218	0.634218	0.126844
0.1	0.126844	4	0.507374	0.607374	0.121475
0.1	0.121475	4	0.485899	0.585899	0.11718
0.1	0.11718	4	0.468719	0.568719	0.113744
0.1	0.113744	4	0.454976	0.554976	0.110995
0.1	0.110995	4	0.44398	0.54398	0.108796
0.1	0.108796	4	0.435184	0.535184	0.107037
0.1	0.107037	4	0.428147	0.528147	0.105629
0.1	0.105629	4	0.422518	0.522518	0.104504
0.1	0.104504	4	0.418014	0.518014	0.103603
0.1	0.103603	4	0.414412	0.514412	0.102882
0.1	0.102882	4	0.411529	0.511529	0.102306
0.1	0.102306	4	0.409223	0.509223	0.101845
0.1	0.101845	4	0.407379	0.507379	0.101476
0.1	0.101476	4	0.405903	0.505903	0.101181
0.1	0.101181	4	0.404722	0.504722	0.100944
0.1	0.100944	4	0.403778	0.503778	0.100756
0.1	0.100756	4	0.403022	0.503022	0.100604
0.1	0.100604	4	0.402418	0.502418	0.100484
0.1	0.100484	4	0.401934	0.501934	0.100387
0.1	0.100387	4	0.401547	0.501547	0.100309
0.1	0.100309	4	0.401238	0.501238	0.100248

After 30 mts CO2 in the room is 0.10025%

After 3mts the CO2 in the room is 0.2024%

After 4 mts it would be 0.1819 %

so After 3.5 mts the CO2 would be reached to 0.2%